The invention relates to new and useful improvements to the transformation of fuzzy logic, which is used to simulate a technical process, into a neural network.
In neuro-fuzzy systems, the input/output response of fuzzy systems can be optimized using neural networks. This makes it possible to compensate for the disadvantages of fuzzy systems and those of neural networks. One option for using a neural network to optimize a fuzzy system is to transform a fuzzy system into a neural network, which is then trained using input/output measured values. While the system response of the technical process that is to be simulated can be reflected in the fuzzy system, the transformation into a neural network allows additional optimization using input/output measured values from the technical process to be simulated. In this case, the optimization process can be automated using optimization algorithms, which can be executed by the neuro-fuzzy system using a computer.
Various methods are known for transforming the components of a fuzzy system into the structures of a neural network. In particular, a fuzzy system has fuzzy logic which, as a rule, is composed of the three components xe2x80x9cfuzzificationxe2x80x9d, xe2x80x9ccontrolxe2x80x9d and xe2x80x9cdefuzzificationxe2x80x9d. The three components can each be modeled using specific types of neurons. The fundamental design of a neuro-fuzzy system, i.e., the individual components of the fuzzy logic within a neuro-fuzzy network, is shown in FIG. 1. When the fuzzy logic FS is being transformed into the neural network NN, the fuzzification F, control base R and defuzzification D components in the neural network NN are represented as a neural fuzzification network NF, a neural control base network NR and a neural defuzzification network ND.
As a result of linguistic rules in the fuzzy logic FS, the control base R component, in particular, results in a number of linguistic values being emitted to the defuzzification D component. The result of a linguistic rule is always a linguistic value. The linguistic values, which are preferably single-element functions, are then united in the defuzzification D component, by defuzzification, to form a single, xe2x80x9csharpxe2x80x9d value.
By way of example, FIG. 2 shows single-element functions F1, F2 . . . Fm of the type which, as a rule, are first normalized with respect to a first maximum value MW1 of magnitude 1. A singleton position A1, A2 . . . Am and at least one singleton weighting factor R1, R2, R3 . . . Rnxe2x88x921 are respectively assigned to the single-element functions F1 . . . Fm, which are also called xe2x80x9csingletonsxe2x80x9d.
The singleton positions A1 . . . Am represent, in particular, the result of rules contained in the control base R component of the fuzzy logic FS. This corresponds in particular to the xe2x80x9cTHENxe2x80x9d part of so-called linguistic xe2x80x9cIFxe2x80x94THENxe2x80x9d rules, such as xe2x80x9cIF pressure high, THEN explosion hazard highxe2x80x9d. The singleton positions A1 . . . Am may lie in any desired value range.
The singleton weighting factors R1 . . . Rn correspond in particular to the weighting of the xe2x80x9cTHENxe2x80x9d part of a linguistic rule in the control base R component of the fuzzy logic FS. The singleton weighting factors R1 . . . Rn are in this case used to weight the single-element functions F1 . . . Fm, and one single-element function F1 . . . Fm can also be assigned a number of singleton weighting factors R1 . . . Rn. For example, the weighting factors of the rules xe2x80x9cIF pressure high, THEN explosion hazard highxe2x80x9d and xe2x80x9cIF temperature high, THEN explosion hazard highxe2x80x9d both relate to the same single-element function xe2x80x9cexplosion hazardxe2x80x9d with the singleton position xe2x80x9chighxe2x80x9d. In the example in FIG. 2, the two singleton weighting factors R1 and R2 are assigned to the single-element function F1 having the singleton position A1.
The singleton positions A1 . . . Am (weighted with the singleton weighting factors R1 . . . Rn) of the single-element functions F1 . . . Fm are unified, to form a single value y, in the defuzzification D component of the fuzzy logic FS, by defuzzification. This is done, for example, using the so-called height method:   y  =                              ∑                      υ            =            1                    n                ⁢                  R          ⁢                      xe2x80x83                    ⁢                      υ            ·                          A              ⁡                              (                υ                )                                                                          ∑                      υ            =            1                    n                ⁢                  R          ⁢                      xe2x80x83                    ⁢          υ                      =          y1                        ∑                      υ            =            1                    n                ⁢                  R          ⁢                      xe2x80x83                    ⁢          υ                    
By way of example, FIG. 4a shows conventional modeling of the fuzzy logic FS in the neural network NN. An output signal y1 is formed by addition, via a summing neuron S1, from the singleton positions A1 . . . Am weighted with the singleton weighting factors R1 . . . Rn. In this case, each weighting factor R1 . . . Rn is assigned:
y1=(R1xc2x7A1)+(R2xc2x7A1)+(R3xc2x7A2)+ . . . +(Rnxc2x7Am)
for weighting the corresponding singleton position A1 . . . Am. A disadvantage of this transformation method is that one singleton position A1 . . . Am is in each case assigned to each singleton weighting factor R1 . . . Rn for summing by the summing neuron S1. While there is one degree of freedom of m singleton positions A1 . . . Am in the fuzzy logic FS, the neural network NN generally has many degrees of freedom n for the singleton weighting factors R1 . . . Rn.
FIG. 4b shows how the singleton positions A1 . . . Am of the weighting factors R1 . . . Rn are optimized during the training of the neural network NN that is carried out following the transformation. In this case, the values of the individual singleton positions A1 . . . Am are varied. In comparison with a number m of singleton positions A1 . . . Am before optimization, this results in the number n greater than =m of optimized singleton positions B1 . . . Bn after the optimization process. The optimized neural network NN thus generally has more degrees of freedom n than before the optimization in order to form the output signal y1xe2x80x2.
FIG. 5 shows the single-element functions Fxe2x80x21 . . . Fxe2x80x2n transformed back by reverse transformation of the neural network NN into an optimized fuzzy system FS. While the number of single-element functions F1 . . . Fm was m before the transformation, the fuzzy system FS after reverse transformation disadvantageously now has n single-element functions Fxe2x80x21 . . . Fxe2x80x2n. As a rule, n greater than =m, which means that there are usually more single-element functions after reverse transformation than there were before the transformation.
It is disadvantageous that, for example, this may lead to such a neuro-fuzzy system no longer being feasible on standardized, conventionally available fuzzy system software after the optimization process, since such software allows only a specific maximum number of degrees of freedom, that is to say such software can process only a maximum number of singleton positions or single-element functions.
It is therefore a first object of the invention to provide an improved method for transformation of fuzzy logic into a neural network. It is a further, specific object to provide such a method, in which the singleton positions (A1 . . . Am) in the neural network (NN) can be adjusted, in order to optimize this network, such that their number before and after the optimization process remains constant and thus, in any case, subsequent reverse transformation of the neural network (NN) can be carried out to optimize fuzzy logic (FS). This advantageously allows the use of, in particular, standardized fuzzy system software to describe the optimized fuzzy logic (FS).
According to one formulation of the invention, these and other objects are achieved by a method for transforming fuzzy-logic, which is used to simulate a technical process, into a neural network in order to form a defuzzified output value from normalized single-element functions. This method includes:
assigning a singleton position and at least one singleton weighting factor to each of the normalized single-element functions, wherein each of the normalized single-element functions is assigned either a single singleton weighting factor or a group of singleton weighting factors, with at least one of said normalized single-element functions being assigned one such group of singleton weighting factors;
additively linking the singleton weighting factors within each of a plurality of the group of singleton weighting factors, to produce additively linked singleton weighting factors for respective normalized single-element functions;
weighting the single singleton weighting factors and the additively linked singleton weighting factors via corresponding singleton positions; and
additively linking the single singleton weighting factors and the additively linked singleton weighting factors, weighted by the corresponding singleton positions, in order to form the defuzzified output value.
Particularly advantageous refinements of the invention are described in the specification and claimed in various dependent claims.
One advantage of the method according to the invention is that fuzzy logic can be transformed, in particular component-by-component, into a neural network, which can then be optimized as a totality, that is to say by optimizing all the components jointly. Thus, in addition to the system response which can be considered in the fuzzy logic, such as the number of association functions to be used, measurement data relating to the technical process to be simulated can also be introduced into the optimization process for the neural network.
The method according to the invention for transformation of fuzzy logic, which is used to simulate a technical process, into a neural network, has the further advantage that the optimization of the neural network and the corresponding reverse transformation do not change the number of degrees of freedom of the fuzzy logic. In particular, the number of single-element functions or xe2x80x9csingletonsxe2x80x9d present in the defuzzification component of the fuzzy logic advantageously remains unchanged. It is advantageous that, owing to the transformation method according to the invention, the singleton positions A1 . . . Am in the neural network can be varied during its optimization only in such a way that their number remains constant, and the neural network can thus always subsequently be transformed back into optimized fuzzy logic. This advantageously allows standardized fuzzy-system software, in particular, to be used to describe the optimized fuzzy logic.